The case analyzed in this study is a mountain-wave event over New Zealand on 12 July 2014 during the DEEPWAVE campaign, with the topography and study domain shown in Fig. . This case is useful because it combines a clearly observed mountain wave with relatively rare high-frequency in situ measurements near the tropopause. Earlier analyses inferred possible signatures of turbulence impacts on tracer distributions in the UTLS region . Although direct observational evidence of wave breaking was not available, the event provides targeted in situ observations that make it suitable for evaluating how turbulence parameterizations and model resolution affect the simulation of mountain waves in the UTLS.

The synoptic situation during the event was characterized by a trough to the west of New Zealand and a weak low-pressure system to the south of the islands. This configuration produced moderate northwesterly flow across the South Island, i.e., about 10–15 ms-1 at 5 km, oriented perpendicular to the Southern Alps. At tropopause level (around 10 km altitude), winds were also from the northwest, reaching moderate speeds of about 20 ms-1 along the DEEPWAVE flight path. Overall, weak directional shear created favorable conditions for the generation of vertically propagating mountain waves over the South Island.

The DEEPWAVE research flight FF09 was carried out with the DLR Falcon aircraft on 12 July 2014 between 17:15 and 20:15 UTC. The aircraft followed a clockwise rectangular flight track across the South Island to capture the structure of the mountain-wave event (see Fig. ). To sample vertical variability, the flight pattern consisted of two stacked legs separated by approximately 75 min, with the lower level at 360 hPa (7.9 km) and the upper level at 230 hPa (10.9 km). In the southern segment of the track, the lower leg was flown between 17:30 and 17:50 UTC and the corresponding upper leg between 18:47 and 19:07 UTC. In the northern segment, the lower leg took place from 18:12 to 18:32 UTC and the upper leg from 19:27 to 19:47 UTC. These stacked cross sections provide in situ measurements of mountain waves and turbulence signatures near the tropopause and serve as the observational reference for the model evaluation. Importantly, the simulated primary wave during this period is quasi-stationary, with only weak temporal variations in wave amplitude and vertical structure. The observational comparison therefore focuses on the time of the flight transect, which is representative of the modeled flow regime.

The numerical experiments were performed with the ICOsahedral Nonhydrostatic (ICON) model version icon-2024.01-dwd-2.0, operated in both NWP and LES modes. ICON is a fully compressible atmospheric model jointly developed by the German Weather Service and the Max Planck Institute for Meteorology. It employs an icosahedral-triangular grid constructed using geodesic Delaunay triangulation, a height-based vertical coordinate system, and C-grid staggering . The physical parameterizations include the Tiled TERRA land surface scheme , a one-moment cloud microphysics scheme with graupel , the low-level flow blocking component of the subgrid-scale orographic drag scheme , and the ecRad radiation scheme .

A central aim of this study is to assess how the simulation of mountain waves and turbulence in ICON depends on both the choice of turbulence parameterization and the model resolution. Two turbulence schemes are considered: the operational turbulent kinetic energy scheme TKE scheme; and the more recently developed two-energy turbulence scheme 2TE scheme;. The TKE scheme predicts a single turbulent kinetic energy (TKE) and accounts for turbulence generation beyond vertical wind shear through additional empirical source terms for large-scale horizontal shear (HS term) and breaking subgrid-scale mountain waves (SSO term) . Its development and tuning prioritize operational NWP applications, including aviation turbulence products such as eddy dissipation rate (EDR). In contrast, the 2TE scheme predicts two prognostic turbulence energies, enabling a more flexible representation of anisotropic and stably stratified turbulence. The scheme avoids prescribed minimum diffusion coefficients, dynamically adjusts the turbulence length scale, and employs an assumed probability density function (APDF) method to represent buoyancy production. Through this formulation, the 2TE scheme provides a unified framework for representing turbulence, shallow convection, and subgrid-scale cloud processes . Further details on the two turbulence schemes are provided in Appendix .

While the TKE scheme has long been used operationally and the 2TE scheme is currently under development, their performance in simulating mountain waves and associated turbulence in the UTLS has not been systematically evaluated. A further aim of this study is therefore to provide a first evaluation of the 2TE scheme in this regime, to inform its ongoing development. In addition, the sensitivity of these simulations to horizontal and vertical resolution is not well constrained, despite growing use of km-scale NWP. The case is also demanding in its own right: the Southern Alps of New Zealand present three-dimensional, multi-scale terrain, with several ridges of different heights and orientations, in contrast to the isolated or quasi-two-dimensional ridges of many earlier studies, so that waves from several sources interact. This study therefore investigates how the two turbulence schemes, in combination with different resolutions, represent mountain-wave dynamics, turbulence characteristics, and momentum fluxes during the DEEPWAVE case. The different ICON configurations and sensitivity experiments are introduced in the following subsection.

Based on the two turbulence schemes described above, we carried out a set of numerical experiments with varying horizontal and vertical resolutions, complemented by a nested LES and targeted sensitivity runs. The experiments are summarized in Table . Limited-area ICON simulations in NWP mode were conducted at horizontal grid spacings of approximately 2 km (I20-2TE), 1 km (I10-2TE, I10-TKE), and 0.5 km (I05-2TE). All configurations employed 137 vertical levels with spacing increasing from about 20 m near the surface and not exceeding 200 m up to 14 km, a model top at 30 km, and Rayleigh damping above 20 km. The simulations were initialized from IFS analyses at 00:00 UTC on 12 July 2014 and integrated for 24 h, with outputs every 30 min and every 5 min between 17:00 and 20:00 UTC. Among these, the I10-2TE simulation was selected as the reference case for the analysis.

An online nested LES configuration at 130 m (I01-LES) targeted the southern flight segment. The LES was realized with four nested domains down to 130 m, with the outermost nest run using the 2TE scheme and the inner nests employing a Smagorinsky closure. To isolate parameterized sources of turbulence production in the TKE scheme, we additionally performed targeted sensitivity runs at 1 km resolution: one with only subgrid-scale orography activated (I10-TKE-SSO), one with only horizontal-shear production activated (I10-TKE-HS), and one with both terms deactivated (I10-TKE-none).

In addition to local characteristics, we also evaluate bulk characteristics of the simulated gravity wave (GW) field over the Southern Alps, namely the area-averaged vertical fluxes of momentum induced by the waves. For this purpose, the model output on terrain-following levels was interpolated to geometric height levels, and averages were taken over the analysis domain shown in Fig. . The vertical fluxes of horizontal momentum are defined as 1ρu′w′‾=ρ(u-u‾)(w-w‾)‾,ρv′w′‾=ρ(v-v‾)(w-w‾)‾, where overbars denote horizontal means at a given altitude and primes the corresponding perturbations. The total flux magnitude is then given by 2τ=(ρu′w′‾)2+(ρv′w′‾)2.

The variance of vertical velocity, w′2‾, follows as a special case of these definitions. Along with the subgrid-scale TKE, these diagnostics characterize the bulk properties of the GW field and parameterized turbulence across different resolutions and turbulence schemes. In particular, area-averaged momentum fluxes provide a measure of convergence with resolution and are an important target quantity for parameterizations in coarse-resolution models.

The reference simulation I10-2TE reproduces a distinct mountain-wave pattern over the South Island at flight time (18:00 UTC). Horizontal cross-sections of vertical velocity show alternating bands of ascent and descent downstream of the main ridge of the Southern Alps, extending from the mid-troposphere into the lower stratosphere (Fig. ). The wave signal is most pronounced near the southern leg and south of the DEEPWAVE flight track. It is stronger in the troposphere (4 and 8 km) than in the lower stratosphere (11 km). This decrease in amplitude with height reflects partial wave trapping, consistent with the Scorer-parameter analysis in Sect. 3.2 (Fig. ). Note that the dominant waves also increase in horizontal scale between 4 and 8 km.

A vertical cross-section along the southern segment of the flight path at 18:00 UTC highlights the primary wave response above the topography (Fig. c). The transect passes near Mount Cook, New Zealand's highest mountain, at about x = 68 km. Further southeast, at about x = 125 km, it crosses the Two Thumb Range, the last major ridge in this section. A strong mountain wave, with vertical velocities exceeding 3 ms-1, is triggered by the Mount Cook region, while a weaker wave develops above the Two Thumb Range. Both waves propagate into the lower stratosphere and are associated with leeside descent, low-level steepening of the isentropes, and the production of turbulence (subgrid-scale TKE) as seen in Fig. d. Significant turbulence is confined to the ABL and to regions of steep isentropes associated with lee-side flow separation. Note that non-orographic ABL turbulence is weak, as expected for the early morning hours (06:00 local time).

To assess the stationarity of the simulated wave field, the same cross-section is shown at 17:00 and 19:00 UTC (Fig. a, b, e, f). At upper levels, the primary wave over Mount Cook remains largely unchanged, whereas noticeable differences appear further downstream above the Two Thumb Range. Near the surface, the flow over Mount Cook varies between the three times, with associated variations in the parameterized TKE. In summary, the large-scale wave pattern over the Mount Cook region is quasi-stationary, whereas smaller-scale features and the low-level TKE show less stationarity. This temporal variability at lower levels has little effect on the wave maxima near 6 km or the flight-leg altitudes.

Comparison of I10-2TE with observations (Fig. ) shows that the simulated wave amplitude, in terms of vertical velocity perturbations, agrees reasonably well with the observations on the lower flight leg but it is underestimated on the upper leg. A spatial phase mismatch between simulated and observed waves is also apparent, which is to be expected. While the simulated wave field is almost stationary, particularly for the strong wave triggered above Mount Cook, the real atmosphere is likely much less stationary due to multi-scale interactions among a spectrum of gravity waves and turbulent motions. Additional variability is also expected from temporal changes in the upstream profile. Note that the observed wave phases differ between the lower and upper flight legs. These differences are unlikely to reflect a vertical discontinuity; instead, they most likely result from the roughly one-hour time difference between the two legs and the non-stationary nature of the real gravity-wave field.

The horizontal wind along both legs is compared with the observations in Fig.  for the reference simulation I10-2TE at 17:00, 18:00, and 19:00 UTC. The simulated wind direction on the lower leg changes by about 10°h-1, and the simulation agrees most closely with the observations at the output times nearest each crossing (18:00 UTC for the lower leg, 19:00 UTC for the upper leg). The upper-level wind-speed bias (up to about 10 ms-1) is common to all resolutions and to both turbulence schemes (not shown, as the winds are largely insensitive to scheme and resolution), so the upper-leg differences reflect the represented flow rather than the turbulence parameterization, consistent with the nearly identical resolved variances of the two schemes (Sect. ). Part of the observed wind fluctuation is the wave itself (e.g., wind-speed perturbations of about 5 ms-1 and wind-direction perturbations of 10–15° on the upper leg).

In summary, the reference simulation captures a strong vertically propagating mountain wave but shows no evidence of significant wave breaking or turbulence at flight altitudes associated with the dominant wave, consistent with the observations. It provides the baseline for assessing the sensitivity to model resolution and turbulence parameterization presented in the following subsections.

Figure  presents the wave field in terms of vertical velocity and potential temperature. The simulated wave field is strongly affected by horizontal resolution, with substantially more wave activity at finer grid spacing. At 2 km resolution, the horizontal wavelength increases and the gravity wave exhibits a more hydrostatic character, as shorter scales are no longer resolved. This is particularly evident for the wave triggered by the Two Thumb Range. At finer resolution (0.5 km), the waves become more non-hydrostatic, with vertical velocity perturbations more vertically aligned. Importantly, the number of resolved waves increases as the model begins to capture shorter wavelengths. This effect is even more pronounced in the LES at 130 m. The LES further shows that the shortest wavelengths are trapped in the layer of enhanced stability below about 5 km, with a clear example of trapped lee waves in the lee of the Two Thumb Range. Another notable difference between the NWP simulations and the LES is the representation of the flow structure immediately downstream of the mountains (Mount Cook, an intermediate ridge at ∼ 100 km, and the Two Thumb Range). In the NWP runs, the downslope flow penetrates to lower levels than in the LES, which has a significant effect on mountain-wave triggering. These differences are likely due not only to resolution, but also to the different representation of the atmospheric boundary layer and its coupling with the mountain wave e.g.,. For completeness, horizontal cross-sections of the flow at different resolutions are shown in Appendix , confirming the sensitivity of dominant gravity-wave scales to model resolution.

To gain further insight into the wave environment, upstream profiles of wind speed, potential temperature, Brunt–Väisälä frequency, and the Scorer parameter are shown in Fig. . Wind speed increases approximately linearly from about 10 ms-1 at ridge height to nearly 20 ms-1 just below the tropopause at 9 km. In terms of stability, the lower troposphere (below 5 km) is markedly more stable than the upper troposphere above. These two factors combine to produce a decrease of the Scorer parameter with height through much of the troposphere, followed by a recovery to slightly larger values in the lowermost stratosphere. The Scorer parameter profile implies a cut-off wavelength of about 7 km just above ridge level, increasing to roughly 20 km near the tropopause. This vertical structure explains the generation of trapped lee waves in the more stable layer below 5 km and is likely responsible for the reduced simulated wave amplitude at the upper flight leg. In the observations, by contrast, the primary wave keeps a nearly constant horizontal wavelength of about 8 km and a strong signal on the upper leg, indicating that it propagates more freely than the model's Scorer profile would suggest. This difference may in part reflect a bias in the simulated upstream wind and stability profile, which sets the Scorer parameter. Comparison of these simulations with in situ observations along the southern leg (Fig. ) shows that the wave amplitude is reproduced reasonably well on the lower flight leg but underestimated on the upper leg. Among the NWP simulations, the 0.5 km run (I05-2TE) agrees best with the observed amplitudes at the lower level. The LES better reproduces the wavelength and phase than the NWP simulations, but underestimates the amplitude, particularly on the upper leg. These discrepancies likely reflect, among other factors, the non-stationarity of the real wave field compared to the quasi-stationary model simulations. For example, in the 0.5 km run, the simulated wave above Mount Cook at the altitude of the lower flight leg compares reasonably well with the observed wave at the altitude of the upper leg. The underestimation of the simulated amplitude aloft is most likely a matter of wave propagation (as discussed above), not of turbulent dissipation. Given the three-dimensional, multi-scale orography, exact agreement is not expected, in particular downstream of the primary wave, where waves from different ridges interfere.

The sensitivity to vertical resolution was assessed with additional 2TE runs in which the maximum grid spacing below 14 km was set to 400, 200, and 100 m, respectively. The coarsest grid (400 m) shows clear differences from the reference run, particularly in the stratosphere, whereas the 200 and 100 m results are very similar, particularly for the primary mountain wave, indicating near-convergence at 200 m (Fig. ). This finding motivated the choice of a maximum vertical spacing of 200 m as the default in the NWP setup used here.